Summation equation

In mathematics, a summation equation or discrete integral equation is an equation in which an unknown function appears under a summation sign. The theories of summation equations and integral equations can be unified as integral equations on time scales[1] using time scale calculus. A summation equation compares to a difference equation as an integral equation compares to a differential equation.

The Volterra summation equation is:

x ( t ) = f ( t ) + ∑ i = m n k ( t , s , x ( s ) ) {\displaystyle x(t)=f(t)+\sum _{i=m}^{n}k(t,s,x(s))}

where x is the unknown function, and s, a, t are integers, and f, k are known functions.

References

  1. ^ Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Tomasia Kulik, Christopher C. Tisdell, September 3, 2007
  • Summation equations or discrete integral equations


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